Eratosthenes Model Documents

Main Document

The Eratosthenes model displays the shadows cast by two gnomons (sticks) at different locations on Earth. For one gnomon, Sun is directly overhead (as would be the case if the gnomon was on the Tropic of Cancer at the summer solstice). The other gnomon is due north of the first gnomon. The sizes of the gnomons are greatly exaggerated for visibility. This simulation can be used to help illustrate how Eratosthenes was able to measure the diameter of Earth using the shadows cast by two gnomons, one situated due north of the other, on a day when the southerly gnomon cast no shadow at all. The distance between the two gnomons (along Earth's surface) can be adjusted. The length of the shadow is given, and this length can be used to determine the angle between the gnomon lines and from that the circumference (and diameter, radius, etc) of Earth. Earth can be hidden to give a better view of the relevant geometry.

The Eratosthenes model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_astronomy_Eratosthenes.jar file will run the program if Java is installed. EJS is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models.